I really need help on this question
Simplify the expression by using a Double-Angle formula or a Half-Angle Formula
cos^2 0/2-sin^2 0/2
recall that cos 2x = cos^2 x - sin^2 x
To simplify the expression using a double-angle formula or a half-angle formula, we need to identify which formula can be applied here. In this case, the given expression involves cosine and sine squared terms, so we can use the half-angle formula for cosine to simplify it.
The half-angle formula for cosine is given by:
cos^2 (θ/2) = (1 + cos θ)/2
Similarly, for sine squared, we can use the half-angle formula for sine:
sin^2 (θ/2) = (1 - cos θ)/2
Let's apply these formulas to simplify the given expression.
cos^2 (0/2) - sin^2 (0/2)
Using the half-angle formulas, we substitute θ = 0 into the formulas:
cos^2 (0/2) = (1 + cos 0)/2 = (1 + 1)/2 = 1
sin^2 (0/2) = (1 - cos 0)/2 = (1 - 1)/2 = 0
Therefore, the simplified expression is 1 - 0 = 1.